L1-optimal linear programming estimatorfor periodic frontier functions with Holder continuous derivative

TL;DR

This paper introduces an L1-optimal linear programming estimator for smooth periodic frontier functions with Holder continuous derivatives, achieving almost sure convergence and optimal convergence rates.

Contribution

It presents a novel linear programming-based estimator that effectively estimates smooth frontier functions with proven convergence properties.

Findings

L1-error converges to zero almost surely

Convergence rate is proven to be optimal

Estimator covers all points with minimal support

Abstract

We propose a new estimator based on a linear programming method for smooth frontiers of sample points. The derivative of the frontier function is supposed to be Holder continuous.The estimator is defined as a linear combination of kernel functions being sufficiently regular, covering all the points and whose associated support is of smallest surface. The coefficients of the linear combination are computed by solving a linear programming problem. The L1- error between the estimated and the true frontier functionsis shown to be almost surely converging to zero, and the rate of convergence is proved to be optimal.